Both routes can be reasonable, and the right one depends on your situation. A general gynaecologist can do most of the basic evaluation: a pelvic ultrasound, hormone tests such as thyroid and prolactin, confirming ovulation, arranging a tube test, and referring your husband for a semen analysis. Many couples with simple issues, like irregular ovulation, are managed well at this level with ovulation tracking or tablets.
A fertility specialist (reproductive medicine) makes more sense earlier if you are 35 or older, have tried for a year or longer, have known blocked tubes, endometriosis, very low ovarian reserve, a severely abnormal semen report, repeated miscarriages, or have already had a few rounds of ovulation treatment without success.
At 29 and ten months of trying, starting the basic workup with a gynaecologist you trust is sensible, as long as it moves forward with a clear plan and timeline. What matters most is that both partners get tested and that treatment is not repeated for many months without re-evaluation. If the workup shows something specialised, or if a few months of treatment do not help, ask for a referral.